Event structure models often have some constraint which ensures that for each system run it is clear what are the causal predecessors of an event (i.e. there is no causal ambiguity). In this contribution we study what happens if we remove such constraints. We define five different partial order semantics that are intentional in the sense that they refer to syntactic aspects of the model. We also define an observational partial order semantics, that derives a partial order from just the event traces.
It appears that this corresponds to the so-called early intentional semantics; the other intentional semantics cannot be observationally characterized. We study the equivalences induced by the different partial order definitions, and their interrelations.